On the classification of discrete Hirota-type equations in 3D

In the series of recent publications, we have proposed a novel approach to the classification of integrable differential/difference equations in three dimensions based on the requirement that hydrodynamic reductions of the corresponding dispersionless limits are ‘inherited’ by the dispersive equation. Here we extend this to the fully discrete case. Based on the method of deformations of hydrodynamic reductions, we classify 3D discrete integrable Hirota-type equations within various particularly interesting subclasses. Our method can be viewed as an alternative to the conventional multi-dimensional consistency approach.